Nature Of The Blue-Phase-III-Isotropic Critical Point: An Analogy With The Liquid-Gas Transition

The analogy with the liquid-gas critical point is analyzed to clarify the nature of the pretransitional behavior of physical properties in the vicinity of the Blue-Phase-m-isotropic transition in chiral liquid crystalline systems. The analogy is unusual: temperature serves as the ordering field and entropy plays the role of the order parameter. Both mean field and parametric equations of state are formulated in terms of scaling fields. The scaling fields are linear combinations of the physical fields, which are temperature and chirality. It is shown that mixing of the physical field variables naturally leads to a strong asymmetry with respect to the transition temperature in the behavior of the physical properties that cannot be described by simple power laws. While the mean field theory gives a good description of the experimental data, the scaling theory, if one incorporates mixing of the field variables, gives even better agreement with the experimental data, placing this transition in the same universality class as the three-dimensional Ising model

Novel phase-transition behavior in an aqueous electrolyte solution

We have investigated the near-critical behavior of the susceptibility of a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide as a function of the salt concentration. The susceptibility was determined from light-scattering measurements performed at a scattering angle of 90° in the one-phase region near the locus of lower consolute points. A sharp crossover from asymptotic Ising behavior to mean-field behavior has been observed at concentrations ranging from 8 to 16.5 mass% NaBr. The range of asymptotic Ising behavior shrinks with increasing salt concentration and vanishes at a NaBr concentration of about 17 mass%, where complete mean-field-like behavior of the susceptibility is observed. A simultaneous pronounced increase in the background scattering at concentrations above 15 mass%, as well as a dip in the critical locus at 17 mass% NaBr, suggests that this phenomenon can be interpreted as mean-field tricritical behavior associated with the formation of a microheterogeneous phase due to clustering of the molecules and ions. An analogy with tricritical behavior observed in polymer solutions as well as the possibility of a charge-density-wave phase is also discussed. In addition, we, have observed a third soap-like phase on the liquid-liquid interface in several binary and ternary liquid mixtures

Scaling and Crossover to Tricriticality in Polymer Solutions

We propose a scaling description of phase separation of polymer solutions. The scaling incorporates three universal limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the "ideal-gas" limit for the pure-solvent phase, and the tricritical limit for the polymer-rich phase asymptotically close to the theta point. We have also developed a phenomenological crossover theory based on the near-tricritical-point Landau expansion renormalized by fluctuations. This theory validates the proposed scaled representation of experimental data and crossover to tricriticality.Comment: 4 pages, 3 figure

Application of Minimal Subtraction Renormalization to Crossover Behavior near the 3^3He Liquid-Vapor Critical Point

Parametric expressions are used to calculate the isothermal susceptibility, specific heat, order parameter, and correlation length along the critical isochore and coexistence curve from the asymptotic region to crossover region. These expressions are based on the minimal-subtraction renormalization scheme within the $\phi^4$ model. Using two adjustable parameters in these expressions, we fit the theory globally to recently obtained experimental measurements of isothermal susceptibility and specific heat along the critical isochore and coexistence curve, and early measurements of coexistence curve and light scattering intensity along the critical isochore of $^3$He near its liquid-vapor critical point. The theory provides good agreement with these experimental measurements within the reduced temperature range $|t| \le 2\times 10^{-2}$

Competition of Mesoscales and Crossover to Tricriticality in Polymer Solutions

We show that the approach to asymptotic fluctuation-induced critical behavior in polymer solutions is governed by a competition between a correlation length diverging at the critical point and an additional mesoscopic length-scale, the radius of gyration. Accurate light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 200,000 up to 11.4 million clearly demonstrate a crossover between two universal regimes: a regime with Ising asymptotic critical behavior, where the correlation length prevails, and a regime with tricritical theta-point behavior determined by a mesoscopic polymer-chain length.Comment: 4 pages in RevTeX with 4 figure

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

Development of the Algorithmic Basis of the FCAZ Method for Earthquake-Prone Area Recognition

The present paper continues the series of publications by the authors devoted to solving the problem of recognition regions with potential high seismicity. It is aimed at the development of the mathematical apparatus and the algorithmic base of the FCAZ method, designed for effective recognition of earthquake-prone areas. A detailed description of both the mathematical algorithms included in the FCAZ in its original form and those developed in this paper is given. Using California as an example, it is shown that a significantly developed algorithmic FCAZ base makes it possible to increase the reliability and accuracy of FCAZ recognition. In particular, a number of small zones located at a fairly small distance from each other but having a close “internal” connection are being connected into single large, high-seismicity areas

DPS Clustering: New Results

The results presented in this paper are obtained as part of the continued development and research of clustering algorithms based on the discrete mathematical analysis. The article briefly describes the theory of Discrete Perfect Sets (DPS-sets) that is the basis for the construction of DPS-clustering algorithms. The main task of the previously constructed DPS-algorithms is to search for clusters in multidimensional arrays with noise. DPS-algorithms have two stages: the first stage is the recognition of the maximum perfect set of a given density level from the initial array, the second stage is the partitioning of the result of the first stage into connected components, which are considered to be clusters. Study of qualities of DPS-algorithms showed that, in a number of situations in the first stage, the result does not include all clusters which have practical sense. In the second stage, partitioning into connected components can lead to unnecessarily small clusters. Simple variation of parameters in DPS-algorithms does not allow for eliminating these drawbacks. The present paper is devoted to the construction on the basis of DPS-algorithms of their new versions, more free from these drawbacks